Contemporary cardiac and cardiovascular surgical procedures endeavor to accomplish the intended surgical intervention with minimum invasiveness and trauma in order to promote more rapid healing with minimum recuperative discomfort and complications. With improvements in skill and knowledge and surgical instrumentation, many more cardiac and cardiovascular procedures are being successfully achieved while the heart continues to beat, thus obviating complications and increased costs and complexity of transferring a patient to dependence upon a cardiopulmonary bypass machine while the heart is immobilized. Thus, so-called beating-heart surgical procedures on patients are favored where possible, but are nevertheless associated with other difficulties attributable to the dynamics of the continuously moving heart, and with the slippery moist surface of the heart. Various techniques have been attempted to stabilize the heart including applying a suction stabilizer, and installing temporary sutures positioned in tension about target sections of the beating heart. Such techniques are not always reliable in many surgical situations. Another technique to stabilize the heart includes contacting the heart with a fork-like member. However, low coefficient of friction between the moist surface of the heart and the contacting member requires greater normal force to be applied against the surface of the heart to attain adequate stabilization. This results in deformation of the heart chambers which can lead to lowered pumping efficiency and possible arrhythmia. Also, greater normal force applied to the heart can puncture or scrape the heart wall. Accordingly, it would be desirable to provide heart stabilizing apparatus and method for reliable positioning in contact with a beating heart to stabilize at least target sections of the heart during a surgical procedure, using a minimum of normal force applied to the heart via a compliant surface to inhibit perforation or tissue damage, and without causing hematomas in compressed tissue and without significantly interfering with rhythmic beating of the heart muscles.